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Jack can paint a house in 5 days, and Richard can paint the same house in 7 days. Working together, how long will it take them to finish the job?

How do you solve this?



Answer :

Well, their speeds are ([tex]V_1[/tex] is Jack's speed, and [tex]V_2[/tex] is Richard's.
[tex]V_1 = \frac{1}{5} houses/day \\ V_2 = \frac{1}{7} houses/day \\ V = V_1 + V_2 = \frac{1}{5}+\frac{1}{7} = \frac{7+5}{35} = \frac{12}{35}[/tex]
They, together, can paint 12 houses in 35 days. To get a single house, we only have to calculate [tex]\frac{35}{12}[/tex] which is very close to 3 (a bit below)
MNewberry359

Answer:

In 7*5 = 35 days, Jack can paint 7 houses.

In 5*7 = 35 days, Richard can paint 5 houses.

So in 35 days, the two of them can paint 12 houses. To paint just one house, they'll need 1/12 the time, or 35/12 = 2 11/12 days.

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